If \(G\)  is a discrete group acting on \(X\)  by isometries, then the subalgebra of equivariant operators obtained by closing the finite propagation operators that are equivariant, denoted by \(C^{*}X^{G}\)  is also graded by intersecting with the subspaces above. Note that this algebra, if the action is free and proper, is Morita equivalent to the reduced group \(C^{*}\) -algebra of \(G\)  (see for instance [1]} - by no means an original or earliest reference).
